Exact elasto-plastic analysis of rotating disks made of functionally graded materials Mohammad Zamani Nejad a,⇑ , Abbas Rastgoo b , Amin Hadi b a Mechanical Engineering Department, Yasouj University, P. O. Box: 75914-353, Yasouj, Iran b Mechanical Engineering Faculty, University of Tehran, Tehran, Iran article info Article history: Received 2 July 2014 Received in revised form 18 July 2014 Accepted 24 July 2014 Keywords: Rotating disk Functionally graded material (FGM) Elasto-perfectly-plastic Tresca criterion Exact solution abstract Presented in this paper is an exact closed-form analytical solution for elasto-plastic defor- mations and stresses in a rotating disk made of functionally graded materials (FGMs) in which the elasto-perfectly-plastic material model is employed. As for the yield criterion, the well-known Tresca’s model is used. The material properties are assumed to vary according to the power law whereas the Poisson’s ratio is kept constant. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit angular speed, displacement and stresses versus the radial direction. Moreover, the effect of increasing the angular speed on the propagation of the plastic zone is investigated. This analysis reveals that the plasticity can occur in different regions of the disk. To the best of authors’ knowledge, so far all previous exact solutions for the elasto-plastic analysis of FGM disks address the case of constant material density. The novelty of this work is to present an exact solution by taking into account the variation of density. The results show that the variation of density has a significant influence on the distribution of deformations and stresses. Furthermore, the effect of changing Poisson’s ratio on the value of the critical material parameter is demonstrated. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Functionally graded materials (FGMs) are composite materials in which mechanical properties vary smoothly and contin- uously from one surface to the other (Ozturk & Gulgec, 2011). Functional grading of material can be used to achieve a variety of goals, including alleviation of residual stresses, reducing stresses during lifetime of the structure, improvement of stability and dynamic response, preventing fracture and fatigue, etc (Birman, 2014). A number of papers considering various aspects of FGM have been published in recent years (Ghannad, Rahimi, & Nejad, 2013; Kahrobaiyan, Rahaeifard, Tajalli, & Ahmadian, 2012; Lijun, Guansuo, Bingfei, & Libiao, 2014; Simsek & Reddy, 2013; Xue & Pan, 2013). Rotating annular and solid disks are of prac- tical concern in many fields of engineering, such as mechanical, marine, and civil engineering with many industrial applica- tions, including steam and turbo generators, turbojet engines, brake disks, rotors, jet engines, flywheels, automobiles, pumps, centrifugal compressors, circular saws, turbines, CDs and DVDs in data storage, and many other applications. This mechanical part is often used at high angular velocities. Stress analysis of rotating disks has a long history of researches as an important issue in engineering Design. The stresses due to centrifugal load can have important effects on their strength and safety. Thus, determination of stress and displacement fields are serious goals in designing of these structures http://dx.doi.org/10.1016/j.ijengsci.2014.07.009 0020-7225/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel./fax: +98 7412221711. E-mail addresses: m.zamani.n@gmail.com, m_zamani@yu.ac.ir (M.Z. Nejad). International Journal of Engineering Science 85 (2014) 47–57 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci